Optimal Prizes

Consider agents who undertake costly effort to produce stochastic outputs observable by a principal. The principal can award a prize to them with probabilities that depend on their outputs. His goal is to elicit maximal effort from the agents for the least prize. We show that, given a general class Π of probabilistic schemes for awarding the prize and a domain of agents’characteristics on which the goal is to be achieved, there is a natural total order on Π from the principal’s point-ofview; as well as an “approximately -optimal”(if not optimal) scheme in Π, to any desired level of accuracy. By way of illustration, we compute such optimal schemes for certain domains of binary games, i.e., games with two agents, each of whom has two effort levels (low, high). The optimal scheme is a monotonic step function, which is “in between”the well-known “deterministic”and “proportional”prizes. In the special scenario where the competition is over small fractional increments, as happens in the presence of strong contestants whose base levels of production are high even with low effort, it turns out that the optimal scheme awards the prize according to the “log of the odds”, with odds based upon the proportional prize. JEL Classification: C70, C72, C79, D44, D63, D82.